We document a new stylized fact, that the relationship between the volatility of oil futures prices and the slope of the forward curve is nonmonotone and has a V-shape. This pattern cannot be generated by standard models that emphasize storage. We develop an equilibrium model of oil production in which investment is irreversible and capacity constrained. Investment constraints affect firms' investment decisions and imply that the supply elasticity changes over time. Since demand shocks must be absorbed by changes in prices or changes in supply, time-varying supply elasticity results in time-varying volatility of futures prices. Estimating this model, we show it is quantitatively consistent with the V-shape relationship between the volatility of futures prices and the slope of the forward curve.